In this paper we give a linear algorithm to edge partition a toroidal graph, i.e., graph that can be embedded on the orientable surface of genus one without edge crossing, into three forests plus a set of at most three edges. For triangulated toroidal graphs, this algorithm gives a linear algorithm for finding three edge-disjoint spanning trees. This is in a certain way an extension of the well...

In this paper, we present a new graph model of sparse matrix decomposition for parallel sparse matrix–vector multiplication. Our model differs from previous graph-based approaches in two main respects. Firstly, our model is based on edge colouring rather than vertex partitioning. Secondly, our model is able to correctly quantify and minimise the total communication volume of the parallel sparse...

Our main result essentially reduces the problem of finding an edge-decomposition of a balanced r-partite graph of large minimum degree into r-cliques to the problem of finding a fractional r-clique decomposition or an approximate one. Together with very recent results of Bowditch and Dukes as well as Montgomery on fractional decompositions into triangles and cliques respectively, this gives the...

A T -decomposition of a graph G is a set of edge-disjoint copies of T in G that cover the edge set of G. Graham and Häggkvist (1989) conjectured that any 2l-regular graph G admits a T -decomposition if T is a tree with l edges. Kouider and Lonc (1999) conjectured that, in the special case where T is the path with l edges, G admits a T -decomposition D where every vertex of G is the end-vertex o...

The effect of organic phenol on the compressive and flexural strength of a metakaolin based geopolymer is studied. It was found that 12 wt% phenol resins can increase the compressive and flexural strength by 30% and 65% respectively. In addition, the reinforcing effect of phenol resin is higher in Na-PS and Na-PSS type geopolymers rather than Na-PSDS. Two distinct endothermic peaks were detecte...

—This paper proposes an edge detection algorithm based on adaptive threshold which is obtained by histogram matching edge gradient value. The implementation of this algorithm is made up of three procedures: all phase discrete cosine sequency filtering, wavelet decomposition and adaptive threshold processing. The image is decomposed into low frequency and high frequency subbands by using all ph...

It is known that the edge set of a 2-edge-connected 3-regular graph can be decomposed into paths of length 3. W. Li asked whether the edge set of every 2-edge-connected graph can be decomposed into paths of length at least 3. The graphs C3, C4, C5, and K4 − e have no such decompositions. We construct an infinite sequence {Fi}∞i=0 of nondecomposable graphs. On the other hand, we prove that every...

We prove a decomposition result for locally finite graphs which can be used to extend results on edge-connectivity from finite to infinite graphs. It implies that every 4k-edge-connected graph G contains an immersion of some finite 2k-edge-connected Eulerian graph containing any prescribed vertex set (while planar graphs show that G need not contain a subdivision of a simple finite graph of lar...

By applying the Tutte decomposition of 2{connected graphs into 3{block trees we provide unique structural characterizations of several classes of 2{connected graphs, including minimally 2{connected graphs, minimally 2{edge{connected graphs, critically 2{connected graphs, critically 2{edge{connected graphs, 3{edge{connected graphs, 2{connected cubic graphs and 3{connected cubic graphs. We also g...

Edge detection improves image readability and it is an important part of images preprocessing aimed to their segmentation and automatic recognition of their contents. This paper describes selected methods of edge detection in magnetic resonance images, with the emphasis on the wavelet transform use. The first part briefly describes the mathematical background of the wavelet transform, including...